Answer: 102°
Step-by-step explanation:
First and foremost, we should note that an isosceles triangle has two sides that are equal and that the sum of angles in a triangle equals to 180°.
Since we are told that the isosceles triangle has base angles that each measure 39°, the third angle will be:
t + 39° + 39° = 180°
t + 78° = 180°
t = 180° - 78°
t = 102°
The third angle is 102°.
Vertical angles are equal, so
.. 3x +8 = 5x -20
.. 28 = 2x . . . . . . . . add 20-3x
.. 14 = x . . . . . . . . . . divide by 2
Each of the vertical angles is 3*14 +8 = 50°, so the supplementary one is 130°.
.. 5*14 +4y = 130
.. 4y = 60 . . . . . . . . subtract 70
.. y = 15 . . . . . . . . . . divide by 4
The values of interest are
.. x = 14
.. y = 15
A circle with center
and radius
has equation

If we substitute
in this equation, we have

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

The expression simplifies to

The solutions to the associated equation are

So, the parabola is negative between the two solutions:

The first option is correct. See an explanation below.
y = -
x - 34
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 68, 0 ) and (x₂, y₂ ) = (0, - 34 )
m =
=
= - 
the y-intercept = (0, - 34 ) ⇒ c = - 34
y= -
x - 34